SOLUTION: Is this inequality true...prove your answer |U|-|U||U|-|U||≤|U+U|≤|U|+|U

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Question 251466: Is this inequality true...prove your answer
|U|-|U||U|-|U||≤|U+U|≤|U|+|U
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
There are a lot of absolute value signs, so we need to be careful. It appears, that your original expression can be simplified to
/(U)/^2 <= /2U/ <= 2/U/, where / U / means absolute value of U.
Checking some numbers will quickly get the desired answer.
U = 0 -> 0 <= 0 <= 0 [TRUE]
U = 1 -> 1 <= 2 <= 2 [TRUE]
U = 2 -> 4 <= 4 <= 4 [TRUE]
U = 3 -> 9 ~<= 6 <= 6 [FALSE]
The only values of U that will hold appear to be {-2, -1, 0, 1, 2}.
hope that helps.